Cell division angle regulates the tissue mechanics and tunes the amount of cerebellar folding

Modeling has proposed that the amount of neural tissue folding is set by the level of differential-expansion between tissue layers and that the wavelength is set by the thickness of the outer layer. Here we used inbred mouse strains with distinct amounts of cerebellar folding to investigate these predictions. We identified a critical period where the folding amount diverges between the strains. In this period, regional changes in the level of differential-expansion between the external granule layer (EGL) and underlying core correlate with the folding amount in each strain. Additionally, the thickness of the EGL is regionally adjusted during the critical period alongside corresponding changes in wavelength. While the number of SHH-expressing Purkinje cells predicts the folding amount, the proliferation rate in the EGL is the same between the strains. However, regional changes in the cell division angle within the EGL predicts both the tangential-expansion and thickness of the EGL. Cell division angle is likely a tunable mechanism whereby both the level of differential-expansion and thickness of the EGL are regionally tuned to set the amount and wavelength of folding.


Introduction 37
The human cortex and cerebellum are formed into complex folded geometries that provide 38 space for the substantial neural circuits and a gross 3-D compartmentalization of functional 39 circuitry within each structure. Changes to the amount of folding in the brain are associated 40 with intellectual disabilities, epilepsies and other health issues (Flotats-Bastardas et al., 2012;41 Leventer et al., 2010;Raymond et al., 1995). Therefore, determining how the degree of folding 42 is set during development is critical for understanding the functional role of the 3-D partitioning 43 of circuits in the gyri of the cortex and the lobules of the cerebellum. 44

45
Little is known about how the tissue geometries and mechanics work together to set the proper 46 amount of folding during development. The murine cerebellum has 8-10 folds aligned in the 47 anterior-posterior axis in the medial region (vermis). This simple arrangement allows for a 48 precise analysis of the geometric and mechanical regulation of the degree of folding from 49 analysis of sagittal sections. Neural tissues have different geometries and conformations than 50 other tissues that undergo folding-like events during development (Nelson, 2016;Shyer et al., 51 2013;Varner and Nelson, 2014). In the developing brain cells are arraigned, not in simple 52 epithelial layers, but in dynamic and thick laminar structures. The cerebellum is further unique. 53 During the second phase of cerebellar development, it grows through the rapid expansion of a 54 temporary external granule layer (EGL) that covers its entire outer surface. The granule cell 55 progenitors (GCPs) within the EGL are proliferative, motile, and are responsible for most of the 56 cerebellar volume growth and for directing growth primarily in the anterior-posterior axis 57 (Joyner and Bayin, 2022;Lawton et al., 2023;Lawton et al., 2019;Legué et al., , 2015Leto 58 expansion as in FVB/NJ. Therefore, by adjusting both the EGL/core growth ratios and the tissue 239 geometry, a cerebellum can set the level of EGL/core differential-expansion and control the 240 amount of folding in L6-7. 241 242 Within FVB/NJ the three neighboring lobule regions, L4-5, L6-7 and L8, all have very similar 243 EGL/core growth ratios (Supplemental Fig 4C). However, these lobule regions achieve different 244 folding amounts during the critical period with L8 remaining unfolded, L4-5 folding once, and 245 L6-7 folding twice. Therefore, we postulated that the distinct geometry of each lobule region 246 must be defining unique balanced expansion ratios that must be overcome for the individual 247 lobule regions to fold. We focused on Lobule 8 because of its simpler shape. In both strains 248 lobule 8 is largely constrained by the surrounding lobule regions. As a result, its width does not 249 increase as the lobule grows. This non-isometric expansion can be compared with a rectangle 250 that has a fixed width and a growing length (Supplemental Fig 5A,B). For this type of growth, 251 the predicted balanced-expansion profile takes a linear form (Supplemental Fig 5C). We found 252 that in both strains the growth ratio of L8 closely approximates the geometrically determined 253 balanced-expansion profile during the critical period, and as predicted, produces no folding 254 (Supplemental Fig 5D,E). Therefore, while the growth ratios between L4-5, L6-7, and L8 are 255 similar within each strain the resulting level of differential-expansion within each strain is 256 regionally regulated by the distinct tissue geometries of the individual lobule regions. Lastly, the 257 small increase in the folding index observed in L4-5 in C57Bl/6J during the critical period comes 258 from the complex geometry and not the onset of new fissures (Supplemental Fig 5F,G). 259

260
The EGL thickness regionally varies between strains. 261 In bi-layer models of cerebral cortex folding, the thickness of the outer layer has been predicted 262 to regulate the wavelength of the resulting folds with thicker layers predicted to produce 263 greater wavelengths between folds (Tallinen et al., 2014). To test if the thickness of the EGL 264 during the formation of the anchoring centers (base of the fissure) could control the folding 265 wavelength, we measured the thickness of the EGL during the critical period when the first 266 fissure that subdivides L6-7 appears. 267 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023

268
We measured the thickness of the EGL by lobule region at the start and end of the critical 269 period (P5, P7 for C57Bl/6J and P3, P5 for FVB/NJ). The EGL thickness varied across the lobule 270 regions in both strains ( Figure 4A-C, Supplemental Fig 6A). At the start of the critical period, 271 prior to the formation of the anchoring center, the EGL of L6-7, L8 and L9 is thicker in C57Bl/6J 272 than in FVB/NJ. At the end of the critical period, thickness of the EGL in L6, L8, and L9 are 273 unchanged between the strains while the EGL of L7 in C57Bl/6J is thicker compared with FVB/NJ 274 (Supplemental Fig 6A). At the end of the critical period the collective L6-7 is not statistically 275 different between the strains (data not shown). 276 277 We next tested if the EGL thickness varied within the regions of L6-7, those that are exposed 278 (where the fissures will appear) and those that are covered (adjacent to other lobules) (white 279 and cyan in Supplemental 6B). At the start of the critical period the EGL of the exposed region 280 was thinner in both strains than the covered region. However, the difference between the 281 strains was most pronounced in the exposed region with the C57Bl/6J having a thicker EGL than 282 FVB/NJ at the start and end of the critical period. By the end of the critical period the EGL in the 283 covered regions showed no difference in thickness between the strains (Fig. 4D,E). As another 284 way to measure the thickness of the exposed surface of L6-7 we quantified the number of cells 285 per EGL surface length ( Fig 4F). As expected, the C57Bl/6J cerebella had more cells per EGL 286 length in L6-7 than in FVB/NJ, and the density of the EGL between the strains was the same 287 (Supplemental Fig 6C). 288 289

Final Wavelength of Folding in L6-7 is predicted by EGL thickness 290
To test if the thicker EGL in C57Bl/6J results in an increased folding wavelength we measured 291 the direct distance between the anchoring centers shared by both strains at P28 (Fig.4

G-I). 292
Anchoring centers (ACs) largely hold their positions in space and therefore retain the spatial 293 information of the EGL surface from the period when they were placed (Sudarov and Joyner, 294 2007;Szulc et al., 2015). Further, each AC has a robustly stereotyped timing of appearance 295 (Legué et al., 2015). Therefore, the thickness of the EGL at the time of each AC formation 296 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 should contribute to the final wavelength of the enclosed lobule. Since the entire C57Bl/6J 297 cerebellum is only ~72-75% the size of FVB/NJ we used a landmark-based procrustean analysis 298 to correct for the global size difference (Fig 4J). 299 300 Within each strain, each of the ACs showed tight clustering with minimal variation (Fig. 4J and 301 Supplemental Fig 6D-F). Using the positions of the ACs retained in both strains, we measured 302 the wavelength of each lobule as the direct distance between the two ACs on either side of 303 each lobule region. The wavelength of L7 was increased in C57Bl/6J compared to FVB/NJ as 304 predicted while the wavelengths of L1-2 and L3 were decreased in C57Bl/6J. (Fig 4K,  305 Supplemental Figure 6G). The remaining wavelengths were unchanged between the strains 306 even L8 and L9 whose EGL thickness was increased at the start of the critical period. However, 307 only the anterior AC enclosing L7 is generated during the critical period when the EGL thickness 308 is increased in C57Bl/6. The anchoring centers setting the boundaries of the other lobules are 309 formed prior to this critical period. 310 311 An unchanged lobule wavelength predicts that at the time the ACs formed, the EGL in that 312 region had a similar thickness between the strains. Therefore, we chose to measure the EGL 313 thickness of L8 as its wavelength was unchanged between the strains. The Secondary fissure, 314 emerging embryonically (~E18), marks the posterior boundary of L8. The Prepyramidal fissure, 315 marking its anterior limit, is already established in the undivided L6-7-8 region at P1 in FVB/NJ 316 and P2 in C57Bl/6J. Therefore, we measured the EGL thickness of L6-7-8 one day prior (P0 and 317 P1 in FVB/NJ and C57Bl/6J, respectively). The EGL thickness was similar between the strains as 318 predicted; however, the small difference was statistically significant suggesting the EGL in 319 FVB/NJ is ~2µm thicker than in C57Bl/6J. (Supplemental Figure 6I). 320

321
We also measured the folding wavelength in absolute distance, not correcting for size 322 differences, and observed the same pattern of wavelengths across the cerebella (Supplemental 323 Fig 6H). All the measured anchoring centers, save the one marking the anterior boundary of L7, 324 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 are in place prior to the critical period, before any significant differences in the growth ratios of 325 the cerebellum develop ( Fig. 2A)  Since the level of differential expansion and EGL thickness are different between the strains and 329 regionally regulated within the cerebellum, we next sought to determine the cellular 330 mechanism accounting for these differences. We first investigated the cellular players that 331 drive expansion of the EGL and the cerebellum. Purkinje cells provide the mitogen that drives 332 the expansion of GCPs within the EGL through their proliferation (Lawton et al., 2023). Without 333 this cell expansion the folding is severely diminished (Corrales et al., 2006). Purkinje cells also 334 play an important role in scaling other cell populations (interneurons and astrocytes) in the 335 cerebellar cortex to form the appropriate number of cellular partners for functional circuits 336 (Joyner and Bayin, 2022;Willett et al., 2019). Therefore, we investigated if the density of 337 Purkinje cells was different between the strains in a way that could change the level of EGL 338 expansion and therefore the growth ratio, differential expansion, and folding. 339 C57Bl/6J mice compared with FVB/NJ. However, by the end of the critical period, after the 353 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint folding amount has diverged, the density of Purkinje cells equalized between the strains (Fig.  354 5E). A similar pattern was observed in L4-5 and L8 (Supplemental Fig. 7F,G). In addition, the 355 Purkinje cells in L6-7 were tightly distributed with less distances between nearest neighbors in 356 the FVB/NJ than in C57Bl/6J at the start before reaching the same spatial distribution at the end 357 of the critical period (Fig. 5F). 358

359
Calculating the density of Purkinje cells at both the start and end of the critical period as a ratio 360 of each lobule's final density at P28 showed that L6-7 in FVB/NJ is denser throughout the critical 361 period whereas L4-5 and L8 are only higher at the start in FVB/NJ (Supplemental Fig. 7H,I). As 362 the Purkinje cells eventually form a single monolayer throughout the cerebellum, the higher 363 density in FVB/NJ during the critical period of L6-7 could indicate that the regional density of 364 We next addressed whether the difference in Purkinje cell density in L6-7 between strains 369 during the critical period was a result of improper cell sorting or differences Purkinje cell 370 number. One possibility is that a portion of the Purkinje cells in C57Bl/6J are improperly 371 directed to the lobules surrounding L6-7. To test this hypothesis, we determined the percent of 372 all Purkinje cells in L4-5, L6-7, and L8 in each strain at the critical period ( Fig. 5G,H). In C57Bl/6J 373 a greater percentage of the Purkinje cells were located within L4-5 and the percentage in L6-7 374 was reduced compared with FVB/NJ (Fig. 5H). Likewise, the number of Purkinje cells was 375 reduced in L6-7 in C57Bl/6J. However, the number of Purkinje cells was the same between the 376 strains in both L4-5 and L8 (Fig. 5I). We next tested if fewer Purkinje cells are present at the 377 start of cerebellum development in C57Bl/6J, specifically those that will occupy L6-7. We 378 measured the numbers of Purkinje cells at the start of folding (E16.5), which is 3 days after 379 Purkinje cell have been born. We found no difference in the number, density, or distribution of 380 Purkinje cells between strains (Fig 5J-L). 381 382 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10. 1101/2023 The proliferation rate of granule cells does not regulate the level of differential-expansion. 383 Since the number and density of Purkinje cells is reduced in L6-7 in C57Bl/6J compared to 384 FVB/NJ we hypothesized that the proliferation rate of GCPs within the EGL would be reduced, 385 potentially lowering the level of differential-expansion. We measured the proliferation rate 386 [EDU+/P27-] of the GCPs in the exposed surface of L6-7 at the start and end of the critical 387 period (Fig 5M,N). Surprisingly, we found no differences in the rate of proliferation at the start 388 or end of the critical period between strains ( Fig 5O). 389

390
The proliferation of the EGL is constrained to the outer P27-cells of the EGL (oEGL) (green in Fig  391   5M,N). We hypothesized that the oEGL may be larger in FVB/NJ, containing more cells able to 392 proliferate, and leading to more expansion with the same rate of proliferation. However, the 393 oEGL/EGL ratio is the same between the strains (Fig. 5P). These results indicate that cell 394 proliferation within the EGL is not adjusted to set the growth ratios or the resulting level of 395 differential-expansion in L6-7 between the strains. 396 397

Cell division angle predicts EGL tangential expansion and thickness 398
Cell division angle (CDA) within the EGL corresponds to the bias in EGL expansion in the 399 anterior-posterior direction as opposed to the medial-lateral direction during cerebellum 400 development (Legué et al., 2015). Additionally, it was found that removing CHD7 from GCPs 401 affects their division angle -increasing the proportion of cells that divide medial-laterally 402 (Reddy et al., 2021). Under this change the cerebellum showed lobule like folds in a medial-403 lateral pattern. Therefore, we hypothesized that CDA could be a fundamental mechanism to 404 regulate both the level of differential-expansion and the thickness of the EGL, ultimately 405 controlling both the folding amount and folding wavelength. 406

407
We measured the CDA in L4-5, L6-7 and L8 by labeling for Phospho-Histone H3 and determining 408 the division plane in reference to the surface of the cerebellum (Fig 6 A,B). We predicted to find 409 a biases towards vertical divisions (60-90 degrees from the surface) in FVB/NJ given the 410 increased tangential expansion and reduced thickness of its EGL. Excitingly, we found that 411 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. We next tested the relationship of CDA to the tangential expansion of the EGL. We measured 418 the average tangential expansion of the EGL in L4-5, L6-7, and L8 in the cerebella used for the 419 cell division measurements during the critical period. We then ran linear regression analysis 420 using the cell division ratio for each lobule region to predict the tangential expansion of the EGL 421 during the critical period ( Fig 6H). We found a significant fit with a high r-squared value 422 demonstrating that the CDA explains over 90% of the variation in the EGL tangential expansion. 423 Similarly, we tested the relationship of the CDA to the EGL thickness. Again, we found a 424 statistically significant relationship between the division angle and the EGL thickness. However, 425 the CDA only explains some 47% of the variability. This indicates that the CDA is only one factor, 426 of potentially several, that contribute to the regulation of EGL thickness ( Fig 6I). 427 428

Discussion 429
Here we tested multiple predictions for neural tissue folding during cerebellar foliation. We 430 found that the degree of cerebellar folding correlates with regional levels of differential-431 expansion due to changes in both the underlying growth ratio between the EGL and the core 432 and to the geometry of the lobules. We also provided developmental evidence that the folding 433 wavelength is regulated by adjusting the thickness of the EGL at the time of fissure formation. 434 We further propose that the angle of cell division within the EGL is a tunable regulator that 435 affects both the tangential expansion and thickness of the EGL (Fig 7 A-C). 436 437

Gene and time-agnostic approaches allow for studies of cerebellar intrinsic mechanics 438
The gene-agnostic approach allowed an unbiased analysis of the tissue mechanics predicted to 439 regulate the degree of cerebellar folding. We propose that our approach of comparing inbred 440 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint mouse strains provides an approximation of the natural folding variation seen between 441 individuals within a species. Intriguingly, the folding differences studied here are similar to 442 those seen across healthy human populations where global variation is minimal and larger 443 changes in amount are constrained to specific regions (Luders et al., 2006(Luders et al., , 2004Zilles et al., 444 1988). An alternative approach to ours to capture the mechanical regulation of natural folding 445 variation would be to use an outbred strain that has substantially more variation between 446 individuals than inbred strains. But without the folding robustness seen in C57Bl/6J and FVB/NJ, The level of Differential-Expansion is regionally adjusted to set the folding amount 459 We uncovered differences in the lobule EGL/core growth ratios and resulting levels of 460 differential expansion between FVB/NJ and C57Bl/6J. First, the tangential expansion of the EGL 461 was increased in FVB/NJ compared to in C57Bl/6J in all lobules measured. The differences in L6-462 7 between the strains was further magnified by the slight geometric difference in the starting 463 shape of L6-7 in each strain. This shape change determines the required ratio of EGL to core 464 growth needed to achieve the same differential-expansion required to lead to folding. In both 465 strains L4-5 and L8 showed very similar growth ratios to L6-7. Yet the divergent geometries 466 significantly modulate the resulting level of differential-expansion needed to produce additional 467 folding. Our data indicates that cerebella can regionally altered both the EGL/core growth ratio 468 and the lobule geometry to adjust the level of cerebellar folding. 469 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint 470 EGL thickness at the time of fissure formation is correlated with the folding wavelength 471 The thickness of the EGL during the critical period was varied within and between the strains, as 472 well as within individual lobules. Excitingly, the significant greater thickness of L6-7 in C57Bl/6 473 compared to FVB/NJ, at the time when the fissures surrounding L7 form, correlates with a 474 longer wavelength of the resulting lobule. In contrast, L8, which showed no difference in the 475 wavelength between strains at P28 had a very similar EGL thickness at the time of fissure 476 formation. The slight difference in thickness detected is a fraction of a single cell diameter and 477 is likely not biologically significant. 478 479 Purkinje cell density during the critical period predicts folding amount 480 Given the role of GCPs in the growth, expansion, and folding of the cerebellum, we predicted 481 that the level of proliferation would be a tunable regulator of the EGL to core growth ratio and 482 therefore of differential-expansion of layers and folding (Corrales et al., 2006;Legué et al., 483 2016). Surprisingly, our data argues that the proliferation rate within the EGL of L6-7, is not 484 tuned to adjust the level tangential expansion of the EGL (Fig 5O). 485

486
In contrast, we found a regional reduction in the number and density of Purkinje cells in L6-7 of 487 C57Bl/6J at the start of the critical period correlating with the future degree of folding (Fig 5E,I). 488 Given that the cerebella of the two strains have the same number of total Purkinje cells in the 489 midline at E16.5 and that the lobules adjacent to L6-7 have comparable numbers of Purkinje 490 cells as their FVB/NJ counterparts during the critical period, we hypothesis that the Purkinje 491 cells in the L6-7 region of C57Bl/6J undergo increased cell death or move a greater distance 492 medial-laterally compared with FVB/NJ mice. 493 494 Surprisingly, Purkinje cell densities at P28 were elevated in C57Bl/6J compared with FVB/NJ. 495 This shows that FVB/NJ achieves more growth per Purkinje cell than C57Bl/6J and suggests that 496 there may be strain intrinsic differences in the degree to which Purkinje cells are able to drive 497 the expansion of other cell populations to scale the proper balance of cells within the 498 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; cerebellum (Joyner and Bayin, 2022;Willett et al., 2019). Indeed, there are many fixed 499 mutational differences between C57Bl/6J and FVB/NJ mice, and indeed, variations also 500 between sub-strains. (Bowes et al., 1990;Kasugai et al., 2007;Mekada and Yoshiki, 2021;501 Schauwecker, 2012;Timmermans et al., 2017). Together, our findings suggests that both the 502 regional number of Purkinje cells during development, as well as their strain intrinsic 503 effectiveness could have a role in scaling the folding of the circuitry. 504 505 Cell division angle as a tunable regulator of the tangential expansion and thickness of the EGL 506 In Lkb1 mutant mice cerebellar folding is increased and EGL thickness is decreased without 507 changing the proliferation rate in the EGL, but with an increase in vertical cell divisions (Ryan et 508 al., 2017). Additionally, lobule-like structures form in the mutant cerebellum in the medial-509 lateral direction when the cell division angle is biased in that direction (Reddy et al., 2021). By 510 shifting the CDA the cerebellum may adjust various mechanical parameters that regulate the 511 degree and wavelength of folding. A horizontal bias should increase the thickness of the EGL at 512 the expense of its tangential expansion. The increased thickness should increase the force 513 required to fold; simultaneously the reduction in tangential expansion will reduce the level of 514 EGL to core differential-expansion, the driving force for folding, and reduce folding (Fig 7A-C). 515 516 Supporting this model, the angle of cell division in the EGL is biased vertically in L6-7 of FVB/NJ 517 compared to C57Bl/6J precisely when we measured a reduced EGL thickness and greater 518 tangential-expansion of the EGL compared to in C57Bl/6 ( Fig. 6C-G). Further, at the start of the 519 critical period in FVB/NJ, there is an increased bias to vertical divisions compared to C57Bl/6J 520 and each lobule region in FVB/NJ has a higher tangential expansion than in C57Bl/6J (Fig 3A,  521 Supplemental Fig 4A,B, 8E). Similarly, at the end of the critical period when L4-5 and L8 have 522 similar division ratios within and between the strains, the resulting EGL thicknesses within and 523 between the strains are similar (Supplemental Fig. 6A, 8A,C). 524 525 While we detected a statistically significant relationship between the angle of cell division and 526 the EGL thickness, it only accounts for 47% of the observed variation in EGL thickness. This 527 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint result predicts that other factors work together with the division angel to tune the EGL 528 thickness. It is plausible that the migration mechanics of GCPs, or their rates of differentiation 529 could play a role. Or it may be that tensile forces, predicted to cross the EGL, may also affect 530 the EGL thickness (Lawton et al., 2019). Excitingly, the cell division angle predicts over 90% of 531 the variation in the tangential expansion of the EGL, suggesting it is a dominant regulator of the 532 tangential expansion and by extension, folding amount of the cerebellum. 533 534 535 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made Center. All data was collected from the two inbred mouse strains, C57Bl/6J (Jackson Labs: 540 000664) and FVB/NJ (Jackson Labs: 001800). Both sexes were used for analysis. Mice were 541 maintained on a 12hr light/dark cycle and food and water were provided ad libitum. was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint Area, Length, Positive curvature, Folding Index measurements, and fissure counts 565 Measurements were collected either in Imaris (Bitplane) or ImageJ as previously described 566 (Lawton et al., 2019). Three midline sections were measured from each cerebellum and the 567 median values were reported. The global length was measured from the anterior start of the 568 surface of the Molecular layer (P28) or the anterior start of the EGL (developmental series). The 569 area was measured by joining the anterior and posterior ends by following the ventricular zone. 570 In ImageJ the positive curvature was created using the convex hull to delete all negative 571 curvature points. Regional, lobule-based measurements were similarly collected. Lobule C57Bl/6J were collected daily from E16.5 to P9 and FVB/NJ were collected daily from E16.5 to 582 P7. For the developmental series 94 cerebella were measured for C57Bl/6J and 96 for FVB/NJ. 583 For each brain in the series the 2-3 most midline sections were measured, and the median 584 values were reported. 585 586 Antibodies and EdU staining 587 Antibody and EdU staining was performed as previously described (Lawton et al., 2019). Prior to 588 IHC EdU was detected using a commercial kit (Invitrogen C10340). Primary antibodies were 589 incubated overnight at 4C or at Room temperature for 4 hours: Goat anti-Foxp2 Everest 590 (1:1000, EB05226), rabbit anti-PH3 EMD Millipore (1:1000, 06-570), Mouse anti-P27 BD 591 Biosciences (1:500, 610241), rabbit anti-Calbindin Swant (1:500, CB38). All antibodies were 592 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint diluted in 2% milk and 0.2% Triton X-100. AlexaFluor secondary antibodies at a 1:1000 dilution 593 were used and sections were counter stained with DAPI. 594 595 Cell Counts, Proliferation, EGL Thickness, Division Angle 596 Purkinje cells were counted in Imaris. Four cerebella were used per strain and per timepoint for 597 developmental stages. For each brain 6-9 midline sections were measured. At P28 five brains 598 were used and four midline sections were measured per brain. The median value for each brain 599 was reported. For E16.5 Measurements four brains were used for C57Bl/6J and three for 600 FVB/NJ and 3 sections per brain were measured. The nearest neighbor analysis was calculated 601 in Imaris software. Matlab (Mathworks) software was used to remove the duplication bias that 602 arose when a pair of cells is nearest neighbors with themselves. 603

604
The Proliferation rate was measured as previously described (Lawton et al., 2019). Four 605 cerebella were used per each strain and per time point. Three midline sections per brain were 606 measured. The median proliferation rate for each brain was reported. All cells within the EGL of 607 the exposed portion of the lobule were measured. DAPI+ cells that were both EDU+ and P27-608 were counted as proliferating. The proliferation rate was calculated as (number of EDU+ cells) / 609 (number of DAPI+; P27-cells). 610

611
The thickness of the EGL was first measured by dividing the area of the EGL by its length. In the 612 L6-7 region the thickness was also measured in the exposed and covered portions of the EGL. 613 Lastly the thickness and density of the exposed region of L6-7 was measured by counting all of 614 the cells within the EGL dividing the counts by the length of the exposed surface. 615

616
The cell division angle was measured in Imaris software. Four brains were measured per strain 617 and per timepoint. For each brain, 6-9 midline sections were measured. The median values per 618 brain were reported. The angle of cell division was measured in relation to the local surface of 619 the EGL. 620 621 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10. 1101/2023 To test the relationship between cell division angle and EGL tangential expansion the cell 622 division angle was measured in L4-5, L6-7 and L8 in four brains at the start of the critical period 623 and the average of the four brains was taken for L4-5, L6-7, and L8. The EGL length was also 624 measured in those brains as well as the four brains at the end of the critical period. The average 625 length difference between the start and end for each lobule region was normalized to control 626 for the differences in their starting sizes. The 6 average cell division ratios (L4-5, L6-7, L8 from 627 C57Bl/6J and FVB/NJ) from the start of the critical period were plotted against the normalized 628 EGL expansion during the critical period. Similarly, the average cell division ration for each 629 lobule region at the start and end of the critical period was plotted against the average EGL 630 thickness measured in the same brains at the start and end. 631 632

Size-free wavelength measurements 633
We used MorphoJ software to run a standard land-mark based procrustean analysis to control 634 for the size difference between the strains (Klingenberg, 2011). We used the 9 conserved 635 anchoring centers as the landmarks and ran standard alignments individually and with strains 636 together. 637 638

Statistics 639
All statistics analyses were run using Matlab (Mathworks). When individual comparisons were 640 made the two-sample t-test was used. The statistical threshold was a p<0.05. When multiple 641 comparisons were being made one-way ANOVA analyses were performed. After ANOVA 642 analysis a multiple comparison was run with Tukey's honestly significant difference criterion. 643 The statistical threshold was set at a p< 0.05. When testing for differences between the strains, 644 the lobule regions, and any interactions, two-way ANOVA analyses was performed and the p-645 values for strain, lobule, and interaction were reported. All error bars are standard deviations. 646 No statistical methods were used to predetermine the sample sizes. We used sample sizes 647 aligned with the standards in the field. No randomization was used nor was data collected or 648 analyzed blind. See statistics table. 649 650 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint

Regression Analyses 651
For the global growth curve fitting we ran non-linear regressions using a basic form of the 652 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made        Interaction terms for differences between L6-7 and L4-5 or L8 reported. E) Calculated slope parameters from linear regression analysis of L4-5, L6-7, and L8 for both strains showing that the slopes are all increased in FVB/NJ compared to C57Bl/6J and the greatest increase is in L6-7. F) Cartoon depicting balanced growth ratio (length/Area) curves for common 2-D shapes. G) The residuals calculated from the predictive growth curves show that the growth ratio of C57Bl/6J is more similar to its balanced growth curve than FVB/NJ. H,I) L6-7 has a slight difference in geometry between the strains with C57Bl/6J having more length per area than FVB/NJ. P-value reported. (mean s.d.) Supplemental Figure 5: Lobule geometry regionally regulates folding amount. A) Sagittal midline sections of L8 region stained with Dapi at the start and end of the critical period in FVB/NJ and C57Bl/6J showing the constraints from the surrounding lobule regions and the limited exposed surface Scale bar: 200µm B) Model of Lobule 8 expansion. The width of the lobule which sets the parameters for the semicircle is fixed while the length is allowed to expand. C) Balanced expansion curves for such constrained shapes are linear and the slope decreases as the fixed width is increased. D) The growth ratio of L8 is well predicted in C57Bl/6J and FVB/NJ by this type of constrained growth showing no evidence of differential-expansion. E) The folding index shows that L8 in both strains remains unfolded as its growth ratios remain balanced. White line: exposed EGL surface. C) EGL density in exposed surface. . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 Supplemental Figure 8: Cell Division Angle is regionally adjusted during the critical period. A-C) Polar plot of cell division angles measured in L4-5, L6-7, and L8 at the start and end of the critical periods. At the end of the critical period the difference between the strains is mostly contained to L6-7. D) Combined cell division angles measured from L4-5, L6-7, and L8. E) Cell division angle ratio of combined data (D). One-way ANOVA p-value reported. Bracket indicates statistical difference. (mean s.d.) . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10.1101/2023.07.21.549165 doi: bioRxiv preprint

7H
Test p-value Test p-value two-way anova one-way anova 3.06E-13 lobules 0 Strain 0 Interaction 0.0002 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted July 21, 2023. ; https://doi.org/10. 1101/2023